Just to be clear, the word "tropical" is sometimes used on auction sites to denote watches (usually Patek Philippe) from the '50s that featured screw-back cases and ceramic dials, as they were considered to be highly impervious to the potentially damaging effects of a tropical climate.

In the sense that you referenced the word, as it pertains to dials, my understanding is that it refers to a type of patina (or degradation) that is typically found as a result of high UV exposure. Such exposure often degraded dials to such a degree that collectors are discouraged. However, a small percentage arguably benefitted from a serendipitous chemical reaction, and such dials are found to be very attractive by collectors.

I have seen this most often with dive watches, for the obvious reason that they were most likely to be over-exposed to UV rays. I currently own one that, to my eye, is quite beautiful. As it is a new acquisition, I haven't yet captured the beauty of the dial in a good image, but this will give you an idea of the effect to which I am referring: